Monday, June 02, 2014

At dinner recently a friend asked, “With pitchers having more Tommy John Surgeries, would making the pitcher’s mound higher change the torque on their elbows?” The fast answer: "In theory. But in practical application? Probably not."

Altering the height of the pitcher's mound is an interesting idea, especially given that the height of the pitching mound hasn't been consistent in the history of Major League Baseball. From the early 1900s until 1968, the pitcher’s mound was 15 inches (depending on the park). 1968 was a a particularly abysmal year in hitting, and MLB changed the rules to lower the pitcher’s mound to 10 inches.

In 1969, William Leggett wrote an article for Sports Illustrated Magazine: From Mountain to Molehill. In it, he mentioned that many pitchers were unhappy with the change and felt unbalanced when they had to adjust their pitching. Pitchers have adjusted since then, and as they are pushed to throw faster and harder, elbow injuries are becoming more common.

There are several factors that can contribute to elbow injuries, and there are two major points of torque on a pitcher’s arm. The shoulder and elbow both experience different amounts of torque at different parts of the throw. Since our original question was specifically focused on the elbow, we’re going to ignore shoulder rotation and only focus on the torque on the elbow.

According to a study published in 2010, Correlation of Torque and Elbow Injury in Professional Baseball Players, there are four ‘events' in the pitching cycle. The one we’re most interested in is seen in the third frame of the picture above. It happens after the wind-up, and is when an over-handed pitcher brings the arm around until right before the ball is released.

When we’re considering this problem we’re going to assume that the forearm is pivoting (along one axis) around the elbow. Pitchers don’t really throw this way, but for an estimation it can help us get the general idea. Torque looks for the force rotating around an axis - exactly what we’re looking for when consider the elbow of a pitcher.

We're only looking at the height of the pitcher's mound (not the slope, that's a different can of worms), and we're making everything else about the pitch the same. The pitcher is throwing the ball with the exact same amount of force on both mounds, and pitching to the exact same point in the strike zone. Assuming Inspector Gadget isn't pitching, the pitcher's arm will stay the same length, so distance will be the same as well. The only thing changing is the angle.

With a higher mound, the pitcher would have to release the ball later to a strike zone that hasn't moved. The angle that the forearm is sweeping through is increasing until release. Because torque only considers a ratio of the angle, with all other things equal, an increase in the angle would reduce the amount of torque on the elbow.

When it comes to real world applications, perhaps the biggest problem with our assumption is that the same amount of force would be applied in both situations. With less torque it might be an 'easier' pitch, and pitchers might compensate by pitching harder. This could perhaps render the effect of a higher mound useless.

More info on the torque estimation for the math-curious:
The calculation for torque is τ = F*d*sinθ. In our example the force the pitcher's using to throw the ball is the same for both mound heights. The distance is the length of the pitcher's forearm from the elbow to the ball, and will stay the same for both pitches. When we increase the angle, the third component of the equation - produces a smaller number. (The sine of 130 degrees is a smaller number than the sine of 100 degrees.) Since F and d are the same in both mound heights, the torque on the pitcher's elbow for a higher mound (with a larger angle) will be less than the torque a pitcher's elbow experiences on the lower mound.